本文主要利用無元素法(Meshfree method)，配合微分再生核近似法(Differential Reproducing Kernel Approximation, DRKM)，加上符合不同邊界條件的應力奇異性項次來分析應力強度因子(stress intensity factor)，計算奇異點附近變化急劇的應力情形，結果發現在加了應力奇異性項次模擬後，將不需要像一般數值方法那麼多的佈點數，就可以有效計算奇異點附近的應力狀態，以及計算應力強度因子。
數值算例中，求解懸臂樑問題時，可以求得最後收斂的各應力強度因子，並說明正確的固定端應力趨勢。對於裂縫問題，計算結果發現可以不需要在奇異點附近加太多的佈點，就能達到理想的精度，最後關於裂縫問題延伸中，說明另一種減少強度因子計算量的方法，也就是在奇異點附近不加密佈點，而只選擇某些點符合控制方程式，藉由如此可減少加密點數，簡化計算量。

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